Question

a2 - 3a + 1=0
find :-
a + 1/a
a2 + 1/a2
a2 = square of a

Answer 1

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Answer 2

Answer:

$\large{\underline{\boxed{\sf \left( a +\dfrac{1}{a} \right) = 3}}}$

$\large{\underline{\boxed{\sf a^2 + \dfrac{1}{a^2} =7}}}$

Step-by-step explanation:

Given that ;

a² - 3a + 1 = 0

⇒ a² - 3a = - 1

⇒ a(a - 3) = - 1

⇒ a - 3 = $\sf -\dfrac{1}{a}$

⇒ a - 3 + $\sf \dfrac{1}{a}$ = 0

⇒ a + $\sf \dfrac{1}{a}$ = 3

Hence, the answer is 3.

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(ii) To find the value of a² + $\sf \dfrac{1}{a^2}$

$\tt \left( a + \dfrac{1}{a} \right) =3$

On squaring both sides ;

$\tt \left( a + \frac{1}{a} \right)^{2} = (3) {}^{2} \\ \\ \rightarrow \tt a^{2} + \frac{1}{ {a}^{2} } + 2 \: . \:a \:. \: \frac{1}{a} = 9 \\ \\ \rightarrow \tt a^{2} + \frac{1}{ {a}^{2} } + 2 = 9 \\ \\ \rightarrow \tt a^{2} + \frac{1}{ {a}^{2} } = 9 - 2 \\ \\ \rightarrow \tt a^{2} + \frac{1}{ {a}^{2} } = 7$

Hence, the answer is 7.